The kit referred to is detailed here:
With its nuts, bolts, gears and moving parts this kaleidoscope will make a cool gift. The kaleidoscope features a classic 3 mirror system to feature a glittering display created by an assortment of multicolored gemstones. The kaleidoscope makes a unique tabletop display with a center body that even
www.pennstateind.com
I have not made this kit but I will tentatively "stick my neck out" and mention the method of end-squaring that I use for pen blanks.
From reading the instructions for this kit, it would seem that the end-squaring of the kaleidoscope blank is more critical than for a pen blank.
The kaleidoscope blank, after rounding, is larger in diameter than usual pen blanks, so my method may not be universally appropriate and depends on the lathe used.
For pen blanks, I square the ends as follows:
1. I mark the center points of both ends of the blank and I mount the blank between centers on my lathe.
2. I turn the pen blank to a cylindrical shape, with the diameter oversize but uniform to better than +/- 0.005".
3. I mount the cylindrical blank in the lathe headstock chuck jaws, carefully ensuring that its axis is coincident with the lathe axis.
4. I mount a cutting tool guide on the tool post accurately perpendicular to the lathe axis.
5. The cutting tool is held firmly against the cutting tool guide but can slide perpendicular to the lathe axis.
6. Material is removed from the end-face of the blank until that end-face is accurately flat (and perpendicular to the lathe axis).
7. Blank is turned end-for-end and the process is repeated for the other end.